Question

One triangle on a graph has a vertical side of 7 and a horizontal side of 12. Another triangle on a graph has a vertical side of 28 and a horizontal side of 48.

Could the hypotenuses of these two triangles lie along the same line?

Yes, because they are similar triangles
Yes, because all triangles can fit along this line
No, because they need to be the same size
No, because they are not similar triangles

Answer 1

i think yes, but idk between a or b

Answer 2

we can speak about a similitude ratio, since the ratio between corresponding sides is:
\[\frac{{48}}{{12}} = \frac{{28}}{7} = ...?\]

Answer 3

more precisely such ratio holds also between the corresponding hypotenuses:

\[\large \begin{gathered}
hypotenus{e_1} = \sqrt {{7^2} + {{12}^2}} = \sqrt {49 + 144} \hfill \\
\hfill \\
\hfill \\
hypotenus{e_2} = \sqrt {{{\left( {4 \times 7} \right)}^2} + {{\left( {4 \times 12} \right)}^2}} = \sqrt {{4^2} \times \left( {{7^2} + {{12}^2}} \right)} = \hfill \\
\hfill \\
= 4\sqrt {{7^2} + {{12}^2}} = 4 \times hypotenus{e_1} \hfill \\
\end{gathered} \]
so the two triangles are similar each other